Abstract: 2D fractured model is generally used for field single fracture created by hydraulic fracturing process. The varied length, height and width of the fracture may affect the accuracy of the fracturing design, causing big difference between designed result and real fracturing effect. This paper deducts and establishes related 3D mathematic model in terms of extending and non-extending upper and lower layers, including presentation of equations of controlling 3D extending of fracture, fracturing fluid flowing pressure drawdown, fractured width and model interpretation. Also, this paper presents the effect of length and orientation of fracture on the reservoir development effectiveness by hydraulic fracturing process and simulation calculation of fracture extending for a multilayer fracturing well. The validity of the model has been proved.

Key words: hydraulic fracturing, fracture, 3D model